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Questions and Answers
Based on the clues, who is the winner of the dessert category in the MasterChef Philippines Contest?
Based on the clues, who is the winner of the dessert category in the MasterChef Philippines Contest?
Sarah is the editor among the neighbors.
Sarah is the editor among the neighbors.
False
What is the age of Ramiro in the Rivera family?
What is the age of Ramiro in the Rivera family?
5
Sean's occupation is __________.
Sean's occupation is __________.
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Match each child with their correct age in the Rivera family:
Match each child with their correct age in the Rivera family:
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Which reasoning involves forming a conclusion based on specific examples?
Which reasoning involves forming a conclusion based on specific examples?
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Deductive reasoning involves forming conclusions from general principles.
Deductive reasoning involves forming conclusions from general principles.
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What is the term used for a conclusion formed through inductive reasoning?
What is the term used for a conclusion formed through inductive reasoning?
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In problem solving, _____ is essential as it helps analyze and reach conclusions.
In problem solving, _____ is essential as it helps analyze and reach conclusions.
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What is the main focus of this chapter on problem solving?
What is the main focus of this chapter on problem solving?
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Match the reasoning type with its description:
Match the reasoning type with its description:
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A logic puzzle can only be solved by applying inductive reasoning.
A logic puzzle can only be solved by applying inductive reasoning.
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What must be pieced together when solving a logic puzzle?
What must be pieced together when solving a logic puzzle?
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Study Notes
Problem Solving & Reasoning - Chapter 3
- Problem solving is a core part of the maths curriculum, vital for success in school and real life.
- Most jobs require good problem-solving skills.
- This chapter aims to improve problem-solving abilities and make it enjoyable.
What is Problem Solving?
- In cognitive psychology, a problem is a mental process people use to discover, analyze, and solve issues.
- George Polya defined problem solving as:
- Finding a way out of difficulty
- Finding a way around an obstacle
- Finding a solution where none is known
- Achieving a desired result not easily attainable
Mathematical Reasoning
- All problem solving, in maths and daily life, involves reasoning.
- Problems often present multiple facts combined to reach a solution.
- Combining reasoning skills with other strategies helps find the solution.
- There are two types of reasoning: inductive and deductive.
Inductive Reasoning
- Inductive reasoning forms a conclusion based on specific examples.
- The conclusion, a conjecture, may or may not be correct.
- Example: predicting the next number in a sequence based on observed patterns.
Example 1 - Inductive Reasoning:
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a. Sequence: 3, 6, 9, 12, 15, ?
- Next number is 18 (adding 3 to the previous number).
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b. Sequence: 1, 3, 6, 10, 15, ?
- Next number is 21 (differences increase by 1 each time).
Example 2 - Inductive Reasoning:
- Procedure: pick a number, multiply by 8, add 6, divide sum by 2, subtract 3.
- Conjecture: The final resulting number is four times the original number.
Deductive Reasoning
- Deductive reasoning reaches a conclusion by applying general principles.
- It's the process of reaching conclusions based on assumptions, procedures, and principles.
Example 3 - Deductive Reasoning:
- Procedure: pick a number, multiply by 8, add 6, divide by 2, subtract 3.
- Deduction: Starting number (n) multiplied by 4 leads to the final result.
Logic Puzzles
- Logic puzzles originate from deduction.
- Solving logic puzzles uses deductive reasoning and organizing information.
- Puzzles often describe events or situations, and clues help determine what happened.
Examples of Logic Puzzles
- Examples include determining the occupations of neighbors or identifying contest winners (MasterChef).
Exercises - Inductive and Deductive Reasoning
- Exercises present scenarios to determine if they are examples of inductive or deductive reasoning.
- Exercises involve determining ages of children based on clues, and identifying correct reasoning methods.
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Description
Explore the fundamentals of problem solving as outlined in Chapter 3 of our math curriculum. This chapter delves into techniques to enhance problem-solving skills and the importance of reasoning in mathematics and real-life situations. Learn about inductive and deductive reasoning methods that aid in arriving at solutions.
